
Then, user 1 adds the first two terms to recover \(W_{\lbrace 1,6\rbrace }\) . User 2 can recover \(W_{\lbrace 2,5\rbrace }\)  by adding \(W_{\lbrace 1,6\rbrace }+W_{\lbrace 2,5\rbrace }+W_{\lbrace 3,4\rbrace }\)  and \(-W_{\lbrace 1,6\rbrace }+W_{\lbrace 2,5\rbrace }-W_{\lbrace 3,4\rbrace }\) , user 3 can recover \(W_{\lbrace 3,4\rbrace }\)  by adding \(W_{\lbrace 1,6\rbrace }+W_{\lbrace 2,5\rbrace }+W_{\lbrace 3,4\rbrace }\)  and \(-W_{\lbrace 1,6\rbrace }-W_{\lbrace 2,5\rbrace }+W_{\lbrace 3,4\rbrace }\) , and so on. We would like to perform the operations (those with \(+\)  and \(-\) ) on a finite field. In other words, with an abuse of notation, we use \(W_{{\mathcal {J}}}\)  to denote both a binary message as well as its representation on a higher field size. We can see that our interference elimination scheme needs a field size larger than 3 (If the field size is 3, \(W_{\lbrace 1,6\rbrace }+W_{\lbrace 2,5\rbrace }+W_{\lbrace 3,4\rbrace }\)  is transmitted to relay 1 and \(W_{\lbrace 1,6\rbrace }+2W_{\lbrace 2,5\rbrace }+2W_{\lbrace 3,4\rbrace }\)  is transmitted to relay 2 such that user 1 add these two sums to get \(2W_{\lbrace 1,6\rbrace }+3W_{\lbrace 2,5\rbrace }+3W_{\lbrace 3,4\rbrace }=2W_{\lbrace 1,6\rbrace }\) ). Since the length of \(W_{{\mathcal {J}}}\) , equal to \({\mathsf {B}}/6\) , goes to infinity as \({\mathsf {B}}\rightarrow \infty \) , we can divide each \(W_{{\mathcal {J}}}\)  where \({\mathcal {J}}\in {\mathcal {V}}_{1}\)  into \(P\)  sub-packets with length \({\mathsf {B}}/(6P)\)  such that we can do operations with field size 3 for sub-packets. Notice that each file is composed of \(6P\)  sub-packets. The link-load to transmit \(W_{{\mathcal {J}}}\)  where \({\mathcal {J}}\in {\mathcal {V}}_{1}\)  is \(P/(6P)=1/6\) . Hence,
the link-load of this scheme is \(2/3\)  while the link-loads of the scheme in Section , in [1]}, [2]} and [3]} are \(3/4\) , \(5/4\) , 1 and 1, respectively.

